MATH 1920 Lecture Notes - Lecture 19: Elementary Function, Antiderivative
11 Oct 2017
School
Department
Course
Professor
Document Summary
Example: find the volume of the tetrahedron with corners at (0, 0, 0), (1, 0, Equation of the tetrahedron: + + = 1. Solving for z: = 1 = (,) Let d be the triangle on the xy-plane with corners (0,0,0), (1,0,0), and (0,1,0) Fix x in the domain [0, 1] and take a slice out of the solid in this plane (where z = 0, so y = 1- x) Vertically simple: = {(,): ,2() :()} Horizontally simple: = {(,): , 2() :()} 1 and = +2 where d is the region between the graphs = : y. Use d as a vertically simple region (notice that it is also horizontally simple, but vertically simple is easier. Points of intersection: (-1, 1) and (2, 4) = {(,): 1 2,: +2}(always use closed bounds) : = {(,):1 4, 2 . 4 the order of integration by thinking about the region we are iterating over.
